What is the polar form of the given complex number without using the argument?

In summary, there is confusion over the correct way to write a given complex number in polar form without using the argument. The attempts made include using a generic 2πn and adding 2π to the argument, but it is uncertain which specific variants are being sought. There is also disagreement on the range of the argument, with some sources using (-π, π] and others using [0, 2π]. Further clarification may be needed from the teacher or the web assign platform.
  • #1
cragar
2,552
3

Homework Statement


Write the given complex number in polar form first using an argument where theta is not equal
to Arg(z)
z=-7i

The Attempt at a Solution


[itex] 7isin(\frac{-\pi}{2}+2\pi n) [/itex]
The weird part about this problem it asks me to not use the argument, The argument is the smallest angle of the complex number, So I added 2 pi to it, but it tells me I am wrong on my web assign, the only other thing I can think of is taking out the generic n and just adding 2 pi to it. [/B]
 
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  • #2
cragar said:
[itex] 7isin(\frac{-\pi}{2}+2\pi n) [/itex]
That's not what I understand by polar form.
 
  • #3
z=x+iy=rcos(x)+irsin(x), that's not polar form
 
  • #4
cragar said:
z=x+iy=rcos(x)+irsin(x), that's not polar form
My mistake, I was thinking of the exponential form.
It's not clear to me which specific variants you tried, like 7i sin(-π/2), 7i sin(3π/2).
As far as I can make out, there is not universal agreement whether Arg is defined to be in the range (-π, π] or [0, 2π).
 
  • #5
I tried 7isin(-pi/2) ,and the one with a generic 2*pi*n, I might have to wait till my teacher gets back to me on e-mail, because I am not sure what my web assign is looking for, I might try 3*pi/2 and then add 2*pi to it, Just wanted to make sure I was interpreting it correctly . thanks for the replies
 

1. What is the Argument of a Complex Number?

The argument of a complex number is the angle between the positive real axis and the line connecting the origin to the complex number in the complex plane. It is usually denoted by the symbol θ or arg(z).

2. How is the Argument of a Complex Number Calculated?

The argument of a complex number can be calculated using the formula arg(z) = arctan(b/a), where a is the real part of the complex number and b is the imaginary part. Alternatively, it can also be calculated using the Pythagorean theorem and trigonometric identities.

3. What is the Range of the Argument of a Complex Number?

The argument of a complex number can have a range from -π to π or from 0 to 2π, depending on the chosen convention. In general, the range of the argument is considered to be a continuous interval of length 2π.

4. What is the Geometric Interpretation of the Argument of a Complex Number?

The argument of a complex number can be interpreted as the angle between the complex number and the positive real axis in the complex plane. This angle also represents the direction or rotation of the complex number from the origin.

5. How is the Argument of a Complex Number Used in Mathematics and Science?

The argument of a complex number is used in various mathematical and scientific applications, such as solving equations involving complex numbers, representing periodic functions, and analyzing the behavior of systems in physics and engineering. It is also an important concept in understanding the properties of complex numbers and their relationship to the polar form of a complex number.

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